Superconductor Analog-to-Digital Converter

ABSTRACT

A superconducting Analog-to-Digital Converter (ADC) employing rapid-single-flux-quantum (RSFQ) logic is disclosed. The ADC has only superconductor active components, and is characterized as being an N th -order bandpass sigma-delta ADC, with the order “N” being at least 2. The ADC includes a sequence of stages, which stages include feedback loops and resonators. The ADC further includes active superconducting components which directionally couple resonator pairs of adjacent stages. The active superconducting components electrically shield the higher order resonator from the lower order resonator. These active superconductor components include a superconducting quantum interference device (SQUID) amplifier, which is inductively coupled to the higher order resonator, and may include a Josephson transmission line (JTL), which is configured to electrically connect the SQUID amplifier to the lower order resonator. The first stage of ADC may employ an implicit feedback loop.

CROSS REFERENCE TO A RELATED APPLICATION

This application is a Continuation of application Ser. No. 11/955,666,filed Dec. 13, 2007, which is incorporated herein by reference in itsentirety.

GOVERNMENT INTERESTS

The invention was produced under U.S. Army CERDEC SBIR ContractsW15P7T-04-C-K605 and DAAB07-03-C-D202, and U.S. Navy ONR ContractN0014-02-C-0171. The United States Government has certain rights in thisinvention.

FIELD OF THE INVENTION

The present invention relates to superconducting electronics. Inparticular, it relates to oversampled Analog-to-Digital Converters.

BACKGROUND OF THE INVENTION

One well-known class of analog-to-digital converters (ADCs) is based onoversampling, in which a single-bit quantizer with feedback is used togenerate a fast bit sequence that can accurately represent an analoginput signal in the band of interest. This requires high sampling rates,for which superconducting electronics is particularly well suited.

The established ΣΔ approach to an oversampling low-pass ADC is based onsigma-delta (ΣΔ) modulation (also called delta-sigma [ΔΣ] modulation),in which the input signal minus a feedback signal is integrated beforequantization. This is well known to result in “noise shaping”, where thequantization noise associated with the data conversion is shiftedoutside the frequency band of interest. The shifted noise may then beeliminated by a subsequent digital filter. This approach has beengeneralized to higher order, with multiple integrators and multiplefeedback loops, by which the noise-shifting is further enhanced. For thehigher order approach to work properly, each integrator must be wellisolated from its neighbor. In conventional semiconductor technology,this isolation is achieved with transistor amplifiers.

A further known generalization of ΣΔ modulators is achieved by replacingthe integrators by high-Q resonators. This suppresses the quantizationnoise at a resonant frequency rather than at low-frequencies, and formsthe basis for a bandpass ADC. Again, improved higher-order performancerequires good isolation between the resonators.

Superconducting circuits based on Josephson junctions, in configurationsknown as rapid single-flux-quantum (RSFQ) logic, can switch on thepicosecond timescale, leading to high sampling rates. Przybysz et al. inU.S. Pat. No. 5,140,324 described a first order, single stage, low-passsigma-delta ADC based on Josephson junctions. Later this was extended toa first order, single stage, bandpass sigma-delta ADC in U.S. Pat. No.5,341,136. Both of these patents are incorporated herein by reference.

Lee et al. in U.S. Pat. No. 6,157,329, incorporated herein by reference,demonstrated that one can avoid a feedback loop in a superconductingbandpass ΣΔ modulator by making use of a special feature of Josephsoncircuits, known as implicit feedback. This technique provides electricalfeedback without an explicit loop. However, this approach is applicableonly to first-order, one stage, feedback. So far a higher order bandpassADC in fully superconducting technology has not been achieved.

SUMMARY OF THE INVENTION

In view of the discussed difficulties, embodiments of the presentinvention disclose a superconducting Analog-to-Digital Converter (ADC)without active semiconductor components, which is characterized as beingan N^(th)-order bandpass sigma-delta ADC. The ADC includes a sequence ofstages, which stages include resonators. Each one of these resonatorsuniquely pertains to one of the stages. The stages number N, with Nbeing at least 2. The stages and the resonators are being characterizedby their order in the sequence, with the order having values from 1through N. The analog signal to be digitized is received by the N-thorder stage. The ADC further includes active superconducting componentsthat directionally couple resonator pairs having adjacent orders. Theactive superconducting components electrically shield the higher orderresonator from the lower order resonator. These active superconductingcomponents include a superconducting quantum interference device (SQUID)amplifier, which is inductively coupled to the higher order resonator,and may include a Josephson transmission line (JTL), which is configuredto electrically connect the SQUID amplifier to the lower orderresonator.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other features of the present invention will become apparentfrom the accompanying detailed description and drawings, wherein:

FIG. 1A shows a schematic diagram of a superconductor N^(th)-orderbandpass sigma-delta ADC according to an embodiment of the presentinvention;

FIG. 1B shows a schematic diagram of an amplification/isolation unit ofthe ADC according to an embodiment of the present invention;

FIG. 2 shows a schematic diagram of a superconductor 2d-order bandpasssigma-delta ADC according to an embodiment of the present invention;

FIG. 3 shows a measured output spectrum for a 7.6 GHz input signal and10.5 GHz sampling rate, showing second-order noise shaping;

FIG. 4 shows a measured power spectrum in a 60 MHz output band afterdigital downconversion and decimation for a 7.6 GHz test signal and 30GHz sampling rate.

DETAILED DESCRIPTION OF THE INVENTION

It is understood that sigma-delta (ΣΔ) analog-to-digital converters(ADC), also known as ΣΔ modulators, or delta-sigma (ΔΣ)modulators/ADC-s, are well known in the electronic arts. Basic conceptsof superconductor ADC-s, meaning ADC-s composed of superconductingcomponents, which components may include both active and passivecomponents, have been discussed already, for instance by O. A. Mukhanovet al. in “Superconductor Analog-to-Digital Converters”, Proc. IEEE,Vol. 92, pp. 1564-1584 (2004).

Briefly, in a low-pass ADC based on sigma-delta (ΣΔ) modulation theinput signal (minus an error feedback signal) is integrated beforequantization. A variation of ΣΔ ADC-s is achieved by replacing theintegrators by resonators. Using a resonator suppresses the quantizationnoise at a resonant frequency rather than at low-frequencies. Such anADC is called in the art a bandpass ADC. For both the low pass,integrator type, and the bandpass, resonator type, ΣΔ ADC-s one canextend the ADC operation to higher order, with multiple stages ofintegrators, or resonators, and with corresponding multiple feedbackloops. Higher order ΣΔ ADC-s enhance performance by shifting noisefurther away from the frequency band of interest. For the properoperation of higher order ADC-s it is desirable that each integrator, orresonator, be well isolated from its lower order neighbor.

With semiconductor technology isolation of successive feedback stages,involving either integrators, or resonators, is quite straightforwarddue to the amplification capabilities of transistors, and bothmultistage low pass and bandpass ΣΔ ADC have been already beenintroduced. However, since superconducting technology lacks a componentsuch as a transistor, in the art it was generally assumed that higherorder ΣΔ ADC are not possible to achieve with superconductivetechnology. See, for instance, discussion in Q. P. Herr, et al., in“Inductive Isolation in Stacked SQUID Amplifiers” IEEE Transactions onApplied Superconductivity, Vol. 17, pp. 565-568, (2007), wheresemiconductor transistors are being applied in a hybridsemiconductor/superconductor technology to realize a low pass, two stageΣΔ ADC.

Embodiments of the present disclosure are characterized as beinghigher-order bandpass sigma-delta ADC-s, employing superconductivetechnology, having only superconductor active components. The use ofsuperconductive technology allows for hitherto unattainable samplingperformance, as characterized by both frequency and accuracy.

The term active superconductor component in this disclosure carries thegeneral accepted meaning used in the art. Active superconductivecomponents generally involve tunnel junctions, most commonly Josephsonjunctions (JJ). Typical active superconductor components include singleJJ-s, Josephson transmission lines (JTL), superconducting quantuminterference devices (SQUID), and various combinations of these.Generally, but not exclusively, active superconducting components havesome kind of bias condition, for instance, and without limitation, acurrent bias. Active semiconductor components, which are absent inembodiments of the present disclosure, have their meaning in the arttypically as transistors and diodes. Active semiconductor componentsusually, but not exclusively, operate under some kind of biasconditions, as well.

FIG. 1A shows a schematic diagram of a superconductor N^(th)-orderbandpass sigma-delta ADC 10 according to a representative embodiment ofthe present invention. The ADC of FIG. 1A receives an RF analog inputsignal 101 and outputs 102 digital pulses, consequently, in thisdisclosure it is usually referred to as a ΣΔ ADC. Such a nomenclature isnot meant to imply limitations. Often, in the art such a structure 10 isnamed ΣΔ modulator, since its digital output 102 is usually furtherprocessed, for instance, deserialized, filtered, etc, before a finalmultibit output is presented as the output of the ADC. For embodimentsof the present invention any and all signal processing, past the digitaloutput 102, are not of major importance, and are not limiting the scopeof the invention.

The schematic of the superconducting bandpass ΣΔ ADC 10 is not unlikethe ones already known in the art. An N^(th) order ADC has N stages. Inembodiments of the present invention, the “N” order of the ADC is atleast 2. The stages are arranged in a sequence, with the stages beingcharacterized by their order in the sequence, from 1 through N. In FIG.1A all repeated components, such as stages, resonators, feedback loops,are indicated with an “i” subscript, with “i” taking on the value of theparticular order. Thus, for instance, resonator 2 being of order of “2”would have the indicator number 12 ₂. The stages 11 _(i) each have aresonator 12 _(i), with each one of the resonators 12 _(i) uniquelypertaining to one of the stages 11 _(i). The analog RF signal to bedigitized is being received 101 by the highest order stage, the onehaving order N. All other stages receive their inputs by combining twosignals. One of these two signals is coming from a feedback loop 13_(i). The other signal of the combination comes from the immediatehigher order stage, through amplification/isolation (A/I) components 14_(i+1,i). Since these A/I components are coupling adjacent order stagepairs, their indicator numbers carry two subscripts, namely the order ofthe coupled stages. Thus, for instance, the A/I coupling stage 3, 11 ₃,to stage 2, 11 ₂, would be indicated as 14 _(3,2).

The output of the first order stage 11 ₁ feeds into a clocked comparator15. The comparator 15 outputs pulses, which pulses then proceed backinto the feedback loops 13 _(i), and to the output 102 of the ADC. Theresonators of the feedback loops 13 _(i) convert the pulses back toanalog signals.

FIG. 1A is only a schematic representation of an N^(th) order ΣΔ ADC 10.Embodiments of the invention may contain additional components, or fewercomponents, as such may be known in the art. Additional components maybe, without limitation, latches, clocks, delay elements in thefeedbacks, and others.

The inductors of the resonators of the ΣΔ modulator/ADC of FIG. 1A, maycontain a string of Josephson junctions. Such a string of Josephsonjunctions due to the nature of superconductivity can be configured toact as a tunable inductor.

In embodiments of the present disclosure all components of the ΣΔ ADC 10are superconductors, used in the general framework of rapidsingle-flux-quantum (RSFQ) technology. The comparator 15 generatessingle-flux-quantum (SFQ) pulses. Using only superconductor activecomponents holds for the A/I 14 _(i+1,i) units. As discussed earlier,the prevailing assumption in the art was that superconducting componentsare not suitable for such a role, primarily because they are not capablefor directional coupling. Without directional coupling, the lower stage11 _(i) may electrically backward disturb the preceding, higher orderstage 11 _(i+1), which may lead to instability in the whole of the ΣΔADC 10.

Embodiments of the present disclosure manifest that a high performancebandpass ΣΔ ADC 10 is achievable with active superconductive componentsin the A/I 14 _(i+1,i) units between successive pairs of stages.

FIG. 1B shows a schematic diagram of an amplification/isolation (A/I)unit of the ADC according to an embodiment of the present invention.Active superconducting components non-reciprocally, directionally,couple pairs of adjacent order resonators 12 _(i), namely, a higherorder resonator and a lower order resonator. The active superconductingcomponents of the A/I 14 _(i+1,i) electrically shield the higher orderresonator 12 _(i+1) from the lower order resonator 12 _(i). The A/I 14_(i+1,i) contains a SQUID amplifier 141. The SQUID amplifier 141 isinductively coupled 144 to the higher order resonator 12 _(i+1). Theinductive coupling 144 is instrumental in the non-reciprocity of thecouplings between successive stages of the ADC. To further enhancedirectionality and the isolation of the higher order stage, a Josephsontransmission line (JTL) 142 may follow the SQUID amplifier 141. The JTL142 may also regenerate and amplify SFQ pulses.

Both the SQUID amplifier 141 and the JTL 142 are well known activesuperconducting components, see, e.g., U.S. Pat. Nos. 4,585,999 and5,936,458, but have not been used in the role as disclosed inrepresentative embodiments of the present invention. The SQUID amplifier141 requires a DC bias to operate, so that it would not functionproperly with a low-pass ADC. This DC bias is not a problem for abandpass ADC, where only alternating currents have to pass along theADC. Also, the SQUID amplifier 141 may have some nonlinearity, adisadvantage for optimum noise suppression. However, in spite of suchpotential difficulties, embodiments of the present disclosure showfunctioning of the bandpass ΣΔ ADC 10 with unprecedented performance.

A superconducting ΣΔ ADC in one respect has a unique advantage comparedto a semiconductor ΣΔ ADC. This advantage is a direct result of thequantum nature of Josephson junctions (JJ). When a JJ clocked through asecond JJ switches, it subtracts a single flux quantum (SFQ=2.07 fWb)from the input while producing a digital output SFQ pulse. Thecomparator 15 of the ΣΔ ADC may use such a two JJ scheme. Thesubtraction of the pulse from the input is precisely what a feedbackloop would be doing in a ΣΔ ADC. Consequently, there may not be a needfor an explicit feedback loop 13 ₁, for the first stage 11 ₁. Thefeedback can be implicit for the first stage 11 ₁. The possibility forsuch an implicit feedback for the first stage in a superconductor ADCusing SFQ technology has already been demonstrated in the art, see forinstance, Lee et al. U.S. Pat. No. 6,157,329. However, the implicitfeedback is useable only for the first stage of a ΣΔ ADC, for higherorder structures, with N being at least 2, one is forced to use explicitfeedback, and the A/I units are unavoidable. Hence, the SFQ pulsesproduced by the comparator 15 have to be propagated back into at least 1of the feedback loops 13 _(i).

FIG. 2 shows a schematic diagram of a superconductor 2d-order bandpasssigma-delta ADC according to an embodiment of the present invention.This 2d-order ΣΔ ADC 100 employs only superconductive technology, havingexclusively superconductive active components. The ADC has tworesonators 121, 122, but only the second stage has an explicit feedbackloop. The feedback of the first stage is implicit. The comparator is aJJ 151, which is clocked through second JJ 152. Such an arrangement hasbeen known in the art. In a niobium (Nb), nominally 1 μm, technologysuch a comparator is capable of a pulse rate close to 50 GHz. With atechnology of submicron groundrules a pulse rate exceeding 100 GHz isachievable. The comparator JJ 151 subtracts a single flux quantum fromthe input while producing a digital output SFQ pulse, and thus, providesfor the implicit feedback.

The signal to be digitized is being received 101 by the second resonator122, while the first resonator 121 feeds into the comparator JJ junction151. The JJ junction comparator 151 is generating SFQ pulses, which aredirected to the second stage feedback loop and to the ADC output 102.

The coupling between the two resonators is accomplished with componentsas discussed in connection with FIG. 1B. A superconducting quantuminterference device (SQUID) 141 amplifier and a Josephson transmissionline (JTL) 142 provide non-reciprocal, directional, coupling between thesecond resonator 122 and the first resonator 121. The SQUID amplifier141 is inductively coupled 144 to the second resonator 122. The JTL 142electrically connects the SQUID amplifier 141 to the first resonator121.

FIG. 2 also shows elements that may typically be present in a secondorder bandpass ΣΔ ADC. Such elements are JTL-s with the purpose of pulseshaping and controlling delay, as total loop delay may need to beadjusted for optimum performance, additional clocks, to adjust phases,and several biasing sources for proper device operation. All of theseare shown for illustrative purposes and without intent of limitation.

As discussed previously, the ΣΔ ADC shown in FIG. 1A and FIG. 2 areoften referred to in the art as ΣΔ modulators because they may beembedded into, and are forming the core of, a larger system. Such asystem may be a digital radio frequency (RF) receiver. For converting anelectromagnetic analog signal into a digital signal, such a RF receivermay use a method involving a representative embodiment of theN^(th)-order bandpass ΣΔ modulator.

Embodiments of the present invention are representative of RSFQ logic,and are not tied to any given superconducting material, or technology.Embodiments practiced with any superconductive material, or materials,including so called high-T_(c) superconductors, are within the scope ofthe present disclosure.

FIG. 3 shows a measured output spectrum of the 2d-order ΣΔ ADC 100 for a7.4 GHz input signal and 10.5 GHz sampling rate, showing second-ordernoise shaping. Given the very high sampling rate, the output of the ADC100 is difficult to measure directly. To demonstrate the performance, aspecial test chip was fabricated that incorporates a deserializer thatreduces the output data rate by a factor of 16. All 16 lines are fed outin parallel to a field-programmable gate array (FPGA) which canreconstruct the data for computation of the power spectrum as shown inFIG. 3. For test purposes a sinusoidal signal at 7.4 GHz was used,together with a clock, or sampling, frequency of f_(clk)=10.5 GHz. Thefirst 121 and the second 122 resonators were set at f₁=7.4 GHz andf₂=7.8 GHz. The correct operation of the ΣΔ ADC 100 is visible by noiseshaped with two dips, near each of the resonant frequencies. Thisdemonstrated the second-order response. Also the input signal shows upas the sharp peak at 7.4 GHz.

Some applications may involve live satellite signals received by anantenna. The output signal of the antenna may be the analog input signalfor the superconducting ΣΔ modulator. The demonstrated sensitivity ofthe ΣΔ modulator/ADC is sufficient for one to feed the analog outputsignal of the antenna directly into the superconducting circuit as ananalog input signal, eliminating the need for inbetween amplification.

FIG. 4 shows a measured power spectrum in a 60 MHz output band afterdigital downconversion and decimation for 7.6 GHz test signal and 30 GHzsampling rate. The power spectrum comes from an X-band all-digitalreceiver implemented as an integrated circuit on a single chip in allsuperconductor Nb technology with 1.5 μm groundrules. At such dimensionsthe JJ critical current, Jc, is 4.5 kA/cm². A sinusoidal test signalenters a 2d-order bandpass ΣΔ ADC 100 such as that of FIG. 2, which ΣΔADC is embedded in the X-band all-digital receiver. The first 121 andthe second 122 resonators were set at f₁=7.4 GHz and f₂=7.6 GHz. Thesignal to noise ratio for a 120 MHz output band is 41 dB, correspondingto 6.5 effective bits, and the spur-free dynamic range (SFDR), a measureof merit known in the art, is 60 dB, corresponding to approximately 10bits.

In the foregoing specification, the invention has been described withreference to specific embodiments. However, one of ordinary skill in theart appreciates that various modifications and changes can be madewithout departing from the scope of the present invention as set forthin the claims below. Accordingly, the specification and figures are tobe regarded in an illustrative rather than a restrictive sense, and allsuch modifications are intended to be included within the scope ofpresent invention.

Benefits, other advantages, and solutions to problems have beendescribed above with regard to specific embodiments. However, thebenefits, advantages, solutions to problems, and any element(s) that maycause any benefit, advantage, or solution to occur or become morepronounced are not to be construed as a critical, required, or essentialfeature, or element, of any or all the claims.

Many modifications and variations of the present invention are possiblein light of the above teachings, and could be apparent for those skilledin the art. The scope of the invention is defined by the appendedclaims.

1. A superconducting circuit, comprising: a sequence of stages, whereinsaid stages comprise resonators, wherein each one of said resonatorsuniquely pertains to one of said stages, wherein said stages number N,with N being at least 2, wherein said stages and said resonators arebeing characterized by an order in said sequence, said order havingvalues from 1 through N, and wherein a stage having N as said order isconfigured to receive an analog input signal; and active superconductingcomponents directionally coupling pairs of said resonators, wherein saidorders of said resonators in said pairs are adjacent to one another,wherein each of said pairs is having a higher order resonator and alower order resonator, wherein said active superconducting componentselectrically shield said higher order resonator from said lower orderresonator.
 2. The superconducting circuit of claim 1, wherein saidactive superconducting components comprise a superconducting quantuminterference device (SQUID) amplifier, wherein said SQUID amplifier isinductively coupled to said higher order resonator.
 3. Thesuperconducting circuit of claim 2, wherein said active superconductingcomponents further comprise a Josephson transmission line (JTL), whereinsaid JTL is configured to electrically connect said SQUID amplifier tosaid lower order resonator.
 4. The superconducting circuit of claim 1,further comprising: feedback loops associated with said stages; and acomparator receiving an input from a stage having 1 as said order,wherein said comparator is generating single flux quantum (SFQ) pulses,and wherein said SFQ pulses are directed to at least 1 of said feedbackloops and to an output for said superconducting circuit.
 5. Thesuperconducting circuit of claim 4, wherein said stage having 1 as saidorder is associated with an implicit feedback loop.
 6. Thesuperconducting circuit of claim 3, wherein said resonators compriseinductors, and at least one of said inductors comprise a string ofJosephson junctions.
 7. The superconducting circuit of claim 1, whereinsaid superconducting circuit is characterized as being an N^(th)-orderbandpass sigma-delta modulator.
 8. A system for digitally receivingradio frequencies, comprising: a superconducting circuit characterizedas being an N^(th)-order bandpass sigma-delta modulator, wherein saidsuperconducting circuit further comprises: a sequence of stages, whereinsaid stages comprise resonators, wherein each one of said resonatorsuniquely pertains to one of said stages, wherein said stages number N,with N being at least 2, wherein said stages and said resonators arebeing characterized by an order in said sequence, said order havingvalues from 1 through N, and wherein a stage having N as said order isconfigured to receive an analog input signal; and active superconductingcomponents directionally coupling pairs of said resonators, wherein saidorders of said resonators in said pairs are adjacent to one another,wherein each of said pairs is having a higher order resonator and alower order resonator, wherein said active superconducting componentselectrically shield said higher order resonator from said lower orderresonator.
 9. The system of claim 8, wherein said active superconductingcomponents comprise a superconducting quantum interference device(SQUID) amplifier, wherein said SQUID amplifier is inductively coupledto said higher order resonator.
 10. The system of claim 9, wherein saidactive superconducting components further comprise a Josephsontransmission line (JTL), wherein said JTL is configured to electricallyconnect said SQUID amplifier to said lower order resonator.
 11. Thesystem of claim 8, wherein said superconducting circuit furthercomprises a comparator receiving an input from a stage having 1 as saidorder, wherein said comparator is generating single flux quantum (SFQ)pulses, wherein said SFQ pulses are directed to at least 1 of saidfeedback loops and to an output for said superconducting circuit. 12.The system of claim 8, wherein said system further comprises an antennaconfigured to receive said radio frequencies and to yield an analogoutput signal.
 13. The system of claim 12, wherein said analog outputsignal is entered directly into said superconducting circuit as saidanalog input signal.
 14. A 2-d order superconducting bandpasssigma-delta modulator, comprising: a first resonator and a secondresonator, wherein an analog signal to be digitized is being received bysaid second resonator; a superconducting quantum interference device(SQUID) amplifier and a Josephson transmission line (JTL), wherein saidSQUID amplifier is inductively coupled to said second resonator, andwherein said JTL electrically connects said SQUID amplifier to saidfirst resonator; a first feedback loop associated with said firstresonator and a second feedback loop associated with said secondresonator, wherein said first feedback loop is an implicit feedbackloop; and a comparator receiving an input from said first resonator,wherein said comparator is generating single flux quantum (SFQ) pulses,wherein said SFQ pulses are directed to said second feedback loop and toan output for said modulator.
 15. A method for converting anelectromagnetic analog signal into a digital signal, said methodcomprising: implementing a superconducting circuit characterized asbeing an N^(th)-order bandpass sigma-delta modulator, and in saidsuperconducting circuit: applying a sequence of resonators, wherein saidresonators number N, characterizing said resonators by an order in saidsequence, said order having values from 1 through N, with N being atleast 2, receiving said analog signal in a resonator having N as saidorder; providing directional coupling with active superconductingcomponents between pairs of said resonators, selecting said orders ofsaid resonators in said pairs to be adjacent to one another, whereineach of said pairs is having a higher order resonator and a lower orderresonator, choosing said directional coupling in a manner to shield saidhigher order resonator from said lower order resonator.
 16. The methodof claim 15, wherein said providing of said directional couplingcomprises inductively coupling a superconducting quantum interferencedevice (SQUID) amplifier to said higher order resonator.
 17. The methodof claim 16, wherein said providing of said directional coupling furthercomprises connecting said SQUID amplifier to said lower order resonatorthrough a Josephson transmission line (JTL).
 18. The method of claim 15,wherein said method further comprises associating said resonators withfeedback loops, and having a comparator generating single flux quantum(SFQ) pulses for at least 1 of said feedback loops and for an output ofsaid superconducting circuit, while a resonator having 1 as said orderis supplying signals for said comparator.
 19. The method of claim 18,wherein said method further comprises associating an implicit feedbackloop with said resonator having 1 as said order.
 20. The method of claim15, wherein said method further comprises providing inductors for saidresonators and to include a string of Josephson junctions in at leastone of said inductors.